結果

問題 No.470 Inverse S+T Problem
コンテスト
ユーザー koyumeishi
提出日時 2016-12-20 02:08:12
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 19 ms / 2,000 ms
コード長 7,519 bytes
コンパイル時間 2,086 ms
コンパイル使用メモリ 137,748 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-12-22 13:18:24
合計ジャッジ時間 3,484 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 27
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
#include <tuple>
#include <utility>
using namespace std;

namespace {
  using Integer = long long; //__int128;
  template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;}
  template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
  template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
  template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;}
  template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
  template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

  template<class H> void print(const H& head){ cout << head; }
  template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
  template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

  template<class H> void eprint(const H& head){ cerr << head; }
  template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
  template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }

  class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator   end(){ return range_iterator(  end_, step_); } };

  inline string operator "" _s (const char* str, size_t size){ return move(string(str)); }
  constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
  constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
  constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

  inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

  mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

  template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); }

  inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; }
}
constexpr long long mod = 9_ten + 7;


class SCC{
  int n;
  vector<vector<int> > G;
  vector<vector<int> > rG;
  
  void dfs(vector<bool> &visit, int pos, vector<int> &result){
    visit[pos] = true;
    for(int i=0; i<G[pos].size(); i++){
      if(visit[ G[pos][i] ]) continue;
      dfs(visit, G[pos][i], result);
    }
    result.push_back(pos);
  }

  void rdfs(vector<bool> &visit, int pos, int k){
    visit[pos] = true;
    component[pos] = k;
    for(int i=0; i<rG[pos].size(); i++){
      if(visit[ rG[pos][i] ]) continue;
      rdfs(visit, rG[pos][i], k);
    }
  }

  void make_rev(vector<vector<int> > &G){
    for(int i=0; i<n; i++){
      for(int j=0; j<G[i].size(); j++){
        rG[ G[i][j] ].push_back(i);
      }
    }
  }

 public:
  int num_components;
  vector<int> component;
  vector< vector<int> > scc_graph;
  
  SCC(int n){
    this->n = n;
    G.resize(n);
    rG.resize(n);
  }

  SCC(vector<vector<int> > &G){
    this->n = G.size();
    this->G = G;
    rG.resize(n);
    make_rev(G);
  }
  
  void strongly_connected_components(){
    vector<bool> visit(n, false);
    vector<int> result;

    for(int i=0; i<n; i++){
      if(visit[i]) continue;
      dfs(visit, i, result);
    }

    
    component.resize(n);
    fill(visit.begin(), visit.end(), false);
    int k=0;
    for(int i=result.size()-1; i>=0; i--){
      if(visit[ result[i] ]) continue;
      rdfs(visit, result[i], k);
      k++;
    }

    num_components = k;
    scc_graph.resize( num_components );
    for(int i=0; i<n; i++){
      int cmp = component[i];
      for(int j=0; j<G[i].size(); j++){
        if(component[ G[i][j] ] == cmp) continue;
        scc_graph[cmp].push_back( component[ G[i][j] ] );
      }
    }
    
    for(int i=0; i<scc_graph.size(); i++){
      sort(scc_graph[i].begin(), scc_graph[i].end());
      scc_graph[i].erase( unique(scc_graph[i].begin(), scc_graph[i].end()), scc_graph[i].end());
    }
    
  }
  
  void add_edge(int from, int to){
    G[from].push_back(to);
    rG[to].push_back(from);
  }
};

void TopologicalSort_dfs(vector<vector<int> > &G, vector<int> &res, int node, vector<bool> &visit){
  if(visit[node] == true) return;
  visit[node] = true;
  for(auto itr = G[node].rbegin(); itr != G[node].rend(); itr++){
    TopologicalSort_dfs(G, res, *itr, visit);
  }
  /*
  for(int i=0; i<G[node].size(); i++){
    TopologicalSort(G, res, G[node][i], visit);
  }
  */
  res.push_back(node);
}

vector<int> TopologicalSort(vector<vector<int>> &G){
  int n = G.size();
  vector<int> ret;
  vector<bool> visit(n,false);
  for(int i=0; i<n; i++){
    if(visit[i]) continue;
    TopologicalSort_dfs(G, ret, i, visit);    
  }
  reverse(ret.begin(), ret.end());
  return ret;
}

int main(){
  int n;
  cin >> n;

  vector<string> u(n);
  cin >> u;

  if(n > 26*2){
    println("Impossible");
    return 0;
  }

  map<string, vector<int>> c;
  for(auto i : range(n) ){
    c[ u[i].substr(0,1) ].push_back( (i+1) );
    c[ u[i].substr(  1) ].push_back( (i+1) );

    c[ u[i].substr(0,2) ].push_back( -(i+1) );
    c[ u[i].substr(  2) ].push_back( -(i+1) );
  }

  vector<vector<int>> G(2*n);

  for(auto p : c){
    if(p.second.size() > 1){
      for(int i=0; i<p.second.size(); i++){
        for(int j=i+1; j<p.second.size(); j++){
          if(i==j) continue;
          int x = p.second[i] < 0 ? -p.second[i]-1 + n : p.second[i]-1;
          int y = p.second[j] < 0 ? -p.second[j]-1 + n : p.second[j]-1;
          G[ (x+n)%(2*n) ].push_back( y );
          G[ (y+n)%(2*n) ].push_back( x );
        }
      }
    }
  }

  SCC scc(G);
  scc.strongly_connected_components();

  bool ok = true;
  for(auto i : range(n) ){
    if(scc.component[i] == scc.component[i+n]) ok = false;
  }

  if(!ok){
    println("Impossible");
    return 0;
  }

  auto& GG = scc.scc_graph;
  auto tp = TopologicalSort(GG);
  vector<int> ord(tp.size());
  for(auto i : range(tp.size()) ){
    ord[ tp[i] ] = i;
  }

  vector<int> ans(n,-1);
  for(int i=0; i<n; i++){
    ans[i] = ord[ scc.component[i] ] < ord[ scc.component[i+n] ] ? 0 : 1;

    string s = ans[i]==0? u[i].substr(0,1) : u[i].substr(0,2);
    string t = ans[i]==0? u[i].substr(1) : u[i].substr(2);
    println(s,t);
  }

  
  return 0;
}
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